Question

The rate constant of a reaction is 5.8 × 10−3 s−1 at 25°c, and the activation energy is 33.6 kj/mol. what is k at 75°c? enter your answer in scientific notation.

Answer 1

Answer:

k₂ = 4.06 x 10⁻² s⁻¹.

Explanation:

• From Arrhenius law: K = Ae(-Ea/RT)

where, K is the rate constant of the reaction.

A is the Arrhenius factor.

Ea is the activation energy.

R is the general gas constant.

T is the temperature.

• At different temperatures:

ln(k₂/k₁) = Ea/R [(T₂-T₁)/(T₁T₂)]

k₁ = 5.8 × 10⁻³ s⁻¹, k₂ = ??? , Ea = 33600 J/mol, R = 8.314 J/mol.K, T₁ = 298.0 K, T₂ = 348.0 K.

• ln(k₂/5.8 × 10⁻³ s⁻¹) = (33600 J/mol / 8.314 J/mol.K) [(348.0 K - 298.0 K) / (298.0 K x 348.0 K)] = (4041.37) (4.82 x 10⁻⁴) = 1.9479.

• Taking exponential of both sides:

(k₂/5.8 × 10⁻³ s⁻¹) = 7.014.

∴ k₂ = 4.06 x 10⁻² s⁻¹.